Low Altitude Rocket Nozzle Design

Dive into the design process, equations and results using the methodology and MATLAB code file below. Join EngineerX in revolutionizing space exploration!  

LOW ATLITUDE ROCKET NOZZLE DESIGN v2.pdf

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Resources 

Low Altitude Conical Nozzle Design Methodology  

In this project, I used MATLAB to design a conical rocket nozzle that meets performance targets at a specified altitude. The design process draws on foundational work by pioneers such as Euler, Prandtl and Tsiolkovsky. Below, I outline the methodology, highlight key results, and share resources for further exploration. Full details are available in the downloadable design process and MATLAB code PDFs. 

The Design Challenge 

Rocket nozzle design hinges on aligning inputs like chamber pressure, temperature, and fuel properties with outputs such as throat diameter, exit geometry, and specific impulse. For this project, we targeted a thrust of 7000N at 5000 m, requiring knowledge of the fuel’s gas constant and specific heat ratio to model exhaust flow accurately.  

While some designs optimize nozzle length or solve for unknown chamber pressure, we used a fixed length of 0.125 m, focusing on tailoring the geometry to maximize thrust efficiency under known conditions. To validate the design, I cross-checked the calculated specific impulse against established values for other nozzles in space, ensuring reliability across altitudes.  

Process Overview 

The MATLAB script implements a 10-step methodology, using equations attributed to pioneers like Prandtl and Tsiolkovsky, to transform inputs into a functional nozzle design: 

• Define Parameters: Specify chamber conditions (pressure, temperature, gas properties), target thrust, and nozzle length, setting the stage for flow calculations. 

• Throat Conditions: Compute pressure, temperature, density, and velocity at the throat (Prandtl/Euler), where flow reaches sonic speed. 

• Atmospheric Conditions: Interpolate ambient pressure and gravity to model external effects on thrust. 

• Exit Mach Number: Solve for the supersonic exit Mach number (Prandtl/Karman), ensuring ideal expansion to match ambient pressure. 

• Expansion Ratio: Determine the area ratio between throat and exit (Prandtl/Glauert), critical for efficient exhaust flow. 

• Exit Conditions: Calculate exit temperature, velocity, and pressure (Prandtl/Karman), defining the exhaust’s contribution to thrust. 

• Nozzle Geometry: Size the throat and exit diameters numerically, optimizing thrust for the fixed length while accounting for divergence losses (Tsiolkovsky/Goddard). 

• Performance Metrics: Evaluate ideal and actual thrust coefficients and specific impulse (Sutton/Tsiolkovsky), quantifying efficiency. 

• Altitude Performance: Assess thrust across various altitudes, ensuring versatility. 

• Visualize Contour: Generate a plot of the nozzle’s conical shape, annotating key dimensions like throat and exit diameters. 

The script employs numerical solvers like fzero for precision and visualizes the nozzle contour, illustrating the geometry that drives performance. 

Key Outcomes 

The nozzle achieves the target thrust with: 

• Throat Diameter: 28.04 mm 

• Exit Diameter: 103.05 mm 

• Expansion Ratio: 13.5022 

• Specific Impulse: 260.78 s 

• Thrust Error: 0.0000% 

  
  

Takeaway  

This project showcases EngineerX’s commitment to advancing space technology and education. The robust MATLAB implementation, tailored for a fixed-length nozzle, demonstrates our ability to solve complex propulsion challenges. By sharing the process and code, we aim to inspire and equip others to explore rocket design.